Sound Pressure

The Sound Pressure is the force of sound on a surface area perpendicular to the direction of the sound.

The Sound Pressure

The Sound Pressure is the force (N) of sound on a surface area (m²) perpendicular to the direction of the sound. The SI-units for the Sound Pressure are N/m² or Pa.

Sound is usually measured with microphones responding proportionally to the sound pressure - p. The power in a sound wave goes as the square of the pressure.

(Similarly, electrical power goes as the square of the voltage.) The log of the square of x is just 2 log x, so this introduces a factor of 2 when we convert to decibels for pressures. The difference in sound pressure level between two sounds with p1 and p2 is therefore:

The Sound Pressure Level

The lowest sound pressure possible to hear is approximately 2 10^-5 Pa (20 micro Pascal, 0.02 mPa), 2 ten billionths of a an atmosphere.

It therefore convenient to express the sound pressure as a logarithmic decibel scale related to this lowest human hearable sound - 2 10^-5 Pa, 0 dB.

The Sound Pressure Level:

L_p = 10 log( p² / p_ref² ) = 10 log( p / p_ref )² = 20 log ( p / p_ref ) (1)

where

L_p = sound pressure level (dB)

p = sound pressure (Pa)

p_ref = 2 10^-5 - reference sound pressure (Pa)

If the pressure is doubled, the sound pressure level is increased with 6 dB ( 20 log (2) ).

Recommended maximum sound pressure level in rooms with different activities.

The table below indicates the sound pressure level in decibel caused by some common sources.

Source	Sound Pressure Level (dB)
Threshold of hearing	0
Rustling leaves	20
Quiet whisper (1 m)	30
Home	40
Quiet street	50
Conversation	60
Inside a car	70
Loud singing	75
Automobile (10 m)	80
Motorcycle (10 m)	88
Food blender (1 m)	90
Subway (inside)	94
Diesel truck (10 m)	100
Lawn mower (1 m)	107
Pneumatic riveter (1 m)	115
Chainsaw (1 m)	117
Amplified Hard Rock (2 m)	120
Jet plane (30 m)	130

Sound power level from some common sources

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